I would not want a .22lr for a coyote. something like the .223/5.56 Nato more ideal for coyotes IMO.

.223
.22-250
.243

Definitely take coyote off of the table if you're considering just a rimfire bunny gun. Take squirrels off of the table if you're planning a proficient coyote rig.

Coyotes go 30lbs, bunnies go 3lbs. Coyotes are typically hunted (called) at 0-200yrds, bunnies are typically hunted under 50yrds. The rifles best suited for each are not the same.

Your post strikes me as "I want to hunt bunnies and squirrels, but I guess maybe someday I'd hunt something bigger..." a lot more than it strikes me as "I need a coyote rifle and a 400yrd prairie dog rifle...".